Standard state of a solution

Sometimes (amount) concentration c is used as a variable in place of molality m both of the above equations then have c in place of m throughout. Occasionally mole fraction x is used in place of m both of the above equations then have x in place of m throughout, and x = 1. Although the standard state of a solute is always referenced to ideal dilute behaviour, the definition of the standard state and the value of the standard chemical potential g are different depending on whether molality m, concentration c, or mole fraction x is used as a variable. 

Recall from Chapters 12 and 13 that the standard state of a substance means a pressure of 1 atm and a specified temperature. In addition, the standard state of a solute is that for which its concentration in ideal solution is 1 M. The standard free energy change AG° for a reaction in which all reactants and products are in their standard states can be calculated from a table of standard free energies of formation AG° of the substances taking part in the reaction (see Appendix D). For reactions that can be carried out in electrochemical cells, the standard free energy change AG° is related to a standard cell voltage A ° by... 

Recall that the standard state of a solute has unit activity, which can differ significantly from 1 M concentration for a real electrolyte solution. In what follows, we will nevertheless refer to 1 M concentration as the standard state. 

In the case of dissolved substances, the standard state of a solute is that in which the effective concentration , known as the activity, is unity. For non-ionic solutes the activity and molarity are usually about the same for concentrations up to about 1M, but for an ionic solute this approximation is generally valid only for solutions more dilute than 0.001-0.0 lAf, depending on electric charge and size of the particular ion. 

Standard Reference Material See certified reference material, standard solution A solution whose composition is known by virtue of the way that it was made from a reagent of known purity or by virtue of its reaction with a known quantity of a standard reagent, standard state The standard state of a solute is 1 M and the standard state of a gas is 1 bar. Pure solids and liquids are considered to be in their standard states. In equilibrium constants, dimensionless concentrations are expressed as a ratio of the concentration of each species to its concentration in its standard state. 

In order to determine the standard molar reaction Gibbs function change ArG°, the standard states of the reaction reactants and products must be defined. They must be chosen or, at a minimum, they must correspond to physical states, such as the physical property differences between them being endowed with an unambiguous physical meaning. As an example, a possible standard state of a solute is the state in which its concentration is 1 mol/L and in which the solution it forms with the solvent is an ideal one. Standard states are chosen conventionally for practical reasons. Fortunately, the conventions are universally agreed upon. 

Solutions in water are designated as aqueous, and the concentration of the solution is expressed in terms of the number of moles of solvent associated with 1 mol of the solute. If no concentration is indicated, the solution is assumed to be dilute. The standard state for a solute in aqueous solution is taken as the hypothetical ideal solution of unit molality (indicated as std. state or ss). In this state... 

But that is not all. For dilute solutions, the solvent concentration is high (55 mol kg ) for pure water, and does not vary significantly unless the solute is fairly concentrated. It is therefore common practice and fully justified to use unit mole fraction as the standard state for the solvent. The standard state of a close up pure solid in an electrochemical reaction is similarly treated as unit mole fraction (sometimes referred to as the pure component) this includes metals, solid oxides etc. 

Standard State of a Solvent in a Mixture The usual choice of a standard state for a solvent in a solution is the pure solvent at a pressure of 1 bar, the same convention as for a pure solid or liquid. Thus,u... 

A note on good practice Recall that the standard state of a pure substance is its pure form at a pressure of 1 bar (Section 6.15). For a solute, the standard state is for a concentration of 1 mol-L 1. Pure solids and liquids may always be regarded as being in their standard states provided the pressure is close to 1 bar. 

In our quantum mechanical solvation modeling,12 27 we take the standard state of the vapor to be a 1 molar ideal gas at 298° K and the standard state of the solute to be a hypothetical 1 molar Henry s law solute at the same... 

In Equation (15.11), the choice of is entirely arbitrary. However, it is conventional to choose m2 =1 mol kg that is, the standard state of the solute is a hypothetical one molal state that is the point of extrapolation of Henry s law behavior to a molality of 1 mol kg In a figure analogous to Figure 15.1, but with ni2 along the horizontal axis, the standard state would be a point on the Henry s law dotted line directly above m2=l mol kg ... 

A more elegant (although more difficult to visualize) formulation of the procedure for the selection of the standard state for a solute may be made as follows. From Eiquation (16.1)... 

Equation (19.19) is consistent with the empirical observation that a nonzero initial slope is obtained when the activity of a ternary electrolyte such as BaCl2 is plotted against the cube of m2/m°). As the activity in the standard state is equal to 1, by definition, the standard state of a ternary electrolyte is that hypothetical state of unit molality ratio with an activity one-fourth of the activity obtained by extrapolation of dilute solution behavior to m2/m° equal to 1, as shown in Eigure 19.4. 

We define the standard state of a liquid as ay = 1 and for gases as an ideal gas pressure of 1 bar, Pj = I- For ideal liquid solutions (activity coefficients of unity), we write ay = Cy so at chemical equilibrium... 

The total entropy of a substance in a state defined as standard. Thus, the standard states of a solid or a liquid are regarded as those of the pure solid or Ihe pure liquid, respectively, and at a stated temperature. The standard state of a gas is at 1 atmosphere pressure and specified temperature, and its standard entropy is the change of entropy accompanying its expansion to zero pressure, or its compression from zero pressure to 1 atmosphere. The standard entropy of an ion is defined in a solution of unit activity, by assuming that the standard entropy of the hydrogen ion is zero. 

Of particular interest is the solvation process that takes place between the standard states of the solute in the ideal gas and in the solution. At a given temperature Tthe ideal gas standard state is specified by the standard pressure, P° = 0.1 MPa (formerly 0.101 325 MPa = 1 atmosphere was generally sped-... 

In order to evaluate each of the derivatives, such quantities as (V" — V-), (S l — Sj), and (dfi t/x t)T P need to be evaluated. The difference in the partial molar volumes of a component between the two phases presents no problem the dependence of the molar volume of a phase on the mole fraction must be known from experiment or from an equation of state for a gas phase. In order to determine the difference in the partial molar entropies, not only must the dependence of the molar entropy of a phase on the mole fraction be known, but also the difference in the molar entropy of the component in the two standard states must be known or calculable. If the two standard states are the same, there is no problem. If the two standard states are the pure component in the two phases at the temperature and pressure at which the derivative is to be evaluated, the difference can be calculated by methods similar to that discussed in Sections 10.10 and 10.12. In the case of vapor-liquid equilibria in which the reference state of a solute is taken as the infinitely dilute solution, the difference between the molar entropy of the solute in its two standard states may be determined from the temperature dependence of the Henry s law constant. Finally, the expression used for fii in evaluating (dx Jdx l)TtP must be appropriate for the particular phase of interest. This phase is dictated by the particular choice of the mole fraction variables. 

Comparison with the standard form for the chemical potential, p = p° + RT In a [Eq. 47 of Chapter 6], shows that in the ideally dilute solution activities are equal to mole fractions for both solvent and solute. In order to find the standard state of the solvent in the ideally dilute solution, we note that at xA = 1 (infinite dilution, within the range of applicability of the model), we have p = p. The standard state of the solvent in the ideally dilute solution is pure solvent, just like the standard states of all components in an ideal solution. The solvent in the ideally dilute solution behaves just like a component of the ideal solution. Although it is also true that p° becomes p at x, = 1, this is clearly outside the realm of applicability of Eq. (43). In order to avoid this difficulty, in determining p° we make measurements at very low values ofx, and extrapolate to x, = 1 using p = p, — RT In x as if the high dilution behavior held to x, = 1. In other words, our standard state for a solute in the ideally dilute solution is the hypothetical state of pure solute with the behavior of the solute in the infinitely dilute solution. 

Why do we not choose the state of infinite dilution as the standard state of the solute in a solution ... 

On the other hand the standard state of a dissolved substance, which behaves in the solvent as a nonelectrolyte, is defined as its state in a hypothetical ideal solution containing one mole of the substance in 1000 grams of solvent (i. e. with a concentration in terms of molality, to = 1). In this solution some properties of the dissolved substance are the same as in an infinitely diluted solution In other cases the hypothetical standard state of the dissolved substance is used in which 1 mole of the substance is contained in one liter of the ideal solution (i. o. the concentration is expressed in terms of molarity, c — 1). 

Employing standard states of a single solute in a physical state of infinite dilution in the liquid stationary phase at the temperature and pressure of the system and a single solute in the perfect gas state at unit pressure and the temperature of the system for the solute in the stationary and in the gaseous phase, respectively, we obtain for the standard molar Gibbs function of sorption of solute i, AG°p(/) [19] ... 

The standard state of a pure substance is defined as that form, at a specified temperature, that is stable at 1 atmosphere pressure (101.325 kPa). For solutes, the standard state is more conveniently defined as a 1 mol L-1 solution of the solute. For chemical reactions in solution, the standard free energy change (AG°) is that for converting 1 mol L"1 of reactants into 1 mol L" 1 of products ... 

Water has an activity of 1 when Nw (see Eq. 2.8) is 1. The concentration of water on a molality basis (number of moles of a substance per kilogram of water for aqueous solutions) is then 1/(0.018016 kg mol-1) or 55.5 molal (m). The accepted convention for a solute, on the other hand, is that aj is 1 when yfj equals 1 m. For example, if yj equals 1, a solution with a 1 -m concentration of solute j has an activity of 1 m for that solute. Thus the standard state for an ideal solute is when its concentration is 1 m, in which case RT In a - is zero.2 A special convention is used for the standard state of a gas such as CO2 or O2 in an aqueous solution—namely, the activity is 1 when the solution is in equilibrium with a gas phase containing that gas at a pressure of 1 atm. (At other pressures, the activity is proportional to the partial pressure of that gas in the gas phase.)... 

In considering the mass law expression, for example, for an acid-base reaction HA = A -I- H, the activities of the solutes are defined in reference to the standard state of a 1-molar concentration. These activities are, in principle, ratios to A" o, HA o, and and are entered in molar units. The... 

Several choices are available in defining the standard state of the solute. If the solute is a liquid which is miscible with the solvent (as, for example, in a benzene-toluene mixture), then the standard state is again the pure liquid. Several different standard states have been used for solutions of solutes of limited solubility. In developing a relationship between drug activity and thermodynamic activity, the pure substance has been used as the standard state. The activity of the dmg in solution was then taken to be the ratio of its concentration to its saturation solubility. The use of a pure substance as the standard state is of course of limited value since a different state is used for each compound. A more feasible approach is to use the infinitely dilute solution of the compound as the reference state. Since the activity equals the concentration in such solutions, however, it is not equal to unity as it should be for a standard state. This difficulty is overcome by defining the standard state as a hypothetical solution of unit concentration possessing, at the same time, the properties of an infinitely dilute solution. Some workers have chosen to... 

Methanol (M) and Formamide (F), relative to a Standard State of Unimolar Solute in Dimethylformamide, at 26°C... 

Solvent activity coefficients for a small number of polar solutes, referred to the standard state of unimolar solute in DMF, are given in Table 3. In the absence of more detailed observations, and applying many of my qualitative observations on the solubility of organic com-poimds, it is tentatively suggested that many polar organic compounds, which are not strong H-bond donors or acceptors, are from 2 to 60 times more solvated by DMF than by methanol or formamide. 

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